3,433 research outputs found
Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics
In this paper, the chaotic ray dynamics inside dielectric cavities is
described by the properties of an invariant chaotic saddle. I show that the
localization of the far field emission in specific directions is related to the
filamentary pattern of the saddle's unstable manifold, along which the energy
inside the cavity is distributed. For cavities with mixed phase space, the
chaotic saddle is divided in hyperbolic and non-hyperbolic components, related,
respectively, to the intermediate exponential (t<t_c) and the asymptotic
power-law (t>t_c) decay of the energy inside the cavity. The alignment of the
manifolds of the two components of the saddle explains why even if the energy
concentration inside the cavity dramatically changes from tt_c, the
far field emission changes only slightly. Simulations in the annular billiard
confirm and illustrate the predictions.Comment: Corrected version, as published. 9 pages, 6 figure
Noise-enhanced trapping in chaotic scattering
We show that noise enhances the trapping of trajectories in scattering
systems. In fully chaotic systems, the decay rate can decrease with increasing
noise due to a generic mismatch between the noiseless escape rate and the value
predicted by the Liouville measure of the exit set. In Hamiltonian systems with
mixed phase space we show that noise leads to a slower algebraic decay due to
trajectories performing a random walk inside Kolmogorov-Arnold-Moser islands.
We argue that these noise-enhanced trapping mechanisms exist in most scattering
systems and are likely to be dominant for small noise intensities, which is
confirmed through a detailed investigation in the Henon map. Our results can be
tested in fluid experiments, affect the fractal Weyl's law of quantum systems,
and modify the estimations of chemical reaction rates based on phase-space
transition state theory.Comment: 5 pages, 5 figure
Reanalysis of the GALLEX solar neutrino flux and source experiments
After the completion of the gallium solar neutrino experiments at the
Laboratori Nazionali del Gran Sasso (GALLEX}: 1991-1997; GNO: 1998-2003) we
have retrospectively updated the GALLEX results with the help of new technical
data that were impossible to acquire for principle reasons before the
completion of the low rate measurement phase (that is, before the end of the
GNO solar runs). Subsequent high rate experiments have allowed the calibration
of absolute internal counter efficiencies and of an advanced pulse shape
analysis for counter background discrimination. The updated overall result for
GALLEX (only) is (73.4 +7.1 -7.3) SNU. This is 5.3% below the old value of
(77.5 + 7.5 -7.8) SNU (PLB 447 (1999) 127-133) with a substantially reduced
error. A similar reduction is obtained from the reanalysis of the 51Cr neutrino
source experiments of 1994/1995.Comment: Accepted by Physics Letters B January 13, 201
Affine T-varieties of complexity one and locally nilpotent derivations
Let X=spec A be a normal affine variety over an algebraically closed field k
of characteristic 0 endowed with an effective action of a torus T of dimension
n. Let also D be a homogeneous locally nilpotent derivation on the normal
affine Z^n-graded domain A, so that D generates a k_+-action on X that is
normalized by the T-action. We provide a complete classification of pairs (X,D)
in two cases: for toric varieties (n=\dim X) and in the case where n=\dim X-1.
This generalizes previously known results for surfaces due to Flenner and
Zaidenberg. As an application we compute the homogeneous Makar-Limanov
invariant of such varieties. In particular we exhibit a family of non-rational
varieties with trivial Makar-Limanov invariant.Comment: 31 pages. Minor changes in the structure. Fixed some typo
Poincare recurrences and transient chaos in systems with leaks
In order to simulate observational and experimental situations, we consider a
leak in the phase space of a chaotic dynamical system. We obtain an expression
for the escape rate of the survival probability applying the theory of
transient chaos. This expression improves previous estimates based on the
properties of the closed system and explains dependencies on the position and
size of the leak and on the initial ensemble. With a subtle choice of the
initial ensemble, we obtain an equivalence to the classical problem of Poincare
recurrences in closed systems, which is treated in the same framework. Finally,
we show how our results apply to weakly chaotic systems and justify a split of
the invariant saddle in hyperbolic and nonhyperbolic components, related,
respectively, to the intermediate exponential and asymptotic power-law decays
of the survival probability.Comment: Corrected version, as published. 12 pages, 9 figure
Roots of the affine Cremona group
Let k[x_1,...,x_n] be the polynomial algebra in n variables and let A^n=Spec
k[x_1,...,x_n]. In this note we show that the root vectors of the affine
Cremona group Aut(A^n) with respect to the diagonal torus are exactly the
locally nilpotent derivations x^a\times d/dx_i, where x^a is any monomial not
depending on x_i. This answers a question due to Popov.Comment: 4 page
Prevalence of marginally unstable periodic orbits in chaotic billiards
The dynamics of chaotic billiards is significantly influenced by coexisting
regions of regular motion. Here we investigate the prevalence of a different
fundamental structure, which is formed by marginally unstable periodic orbits
and stands apart from the regular regions. We show that these structures both
{\it exist} and {\it strongly influence} the dynamics of locally perturbed
billiards, which include a large class of widely studied systems. We
demonstrate the impact of these structures in the quantum regime using
microwave experiments in annular billiards.Comment: 6 pages, 5 figure
New Langevin and Gradient Thermostats for Rigid Body Dynamics
We introduce two new thermostats, one of Langevin type and one of gradient
(Brownian) type, for rigid body dynamics. We formulate rotation using the
quaternion representation of angular coordinates; both thermostats preserve the
unit length of quaternions. The Langevin thermostat also ensures that the
conjugate angular momenta stay within the tangent space of the quaternion
coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have
constructed three geometric numerical integrators for the Langevin thermostat
and one for the gradient thermostat. The numerical integrators reflect key
properties of the thermostats themselves. Namely, they all preserve the unit
length of quaternions, automatically, without the need of a projection onto the
unit sphere. The Langevin integrators also ensure that the angular momenta
remain within the tangent space of the quaternion coordinates. The Langevin
integrators are quasi-symplectic and of weak order two. The numerical method
for the gradient thermostat is of weak order one. Its construction exploits
ideas of Lie-group type integrators for differential equations on manifolds. We
numerically compare the discretization errors of the Langevin integrators, as
well as the efficiency of the gradient integrator compared to the Langevin ones
when used in the simulation of rigid TIP4P water model with smoothly truncated
electrostatic interactions. We observe that the gradient integrator is
computationally less efficient than the Langevin integrators. We also compare
the relative accuracy of the Langevin integrators in evaluating various static
quantities and give recommendations as to the choice of an appropriate
integrator.Comment: 16 pages, 4 figure
GNO Solar Neutrino Observations: Results for GNOI
We report the first GNO solar neutrino results for the measuring period GNOI,
solar exposure time May 20, 1998 till January 12, 2000. In the present
analysis, counting results for solar runs SR1 - SR19 were used till April 4,
2000. With counting completed for all but the last 3 runs (SR17 - SR19), the
GNO I result is [65.8 +10.2 -9.6 (stat.) +3.4 -3.6 (syst.)]SNU (1sigma) or
[65.8 + 10.7 -10.2 (incl. syst.)]SNU (1sigma) with errors combined. This may be
compared to the result for Gallex(I-IV), which is [77.5 +7.6 -7.8 (incl.
syst.)] SNU (1sigma). A combined result from both GNOI and Gallex(I-IV)
together is [74.1 + 6.7 -6.8 (incl. syst.)] SNU (1sigma).Comment: submitted to Physics Letters B, June 2000. PACS: 26.65. +t ; 14.60
Pq. Corresponding author: [email protected] ; [email protected]
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